Try this problem from ISI B.Stat, B.Math Subjective Entrance Exam, 2017 Problem no. 3 based on Differentiability at origin. Problem: Differentiability at origin Suppose \( f : \mathbb{R} \to \mathbb{R} \) is a function given by $$f(x) = \left\{\def\arraystretch{1.2}%\begin{array}{@{}c@{\quad}l@{}}1 & \text{if x=1}\\ e^{(x^{10} -1)} + (x-1)^2 \sin \left (\frac {1}{x-1} \right ) & \text{if} x […]
Let's discuss a beautiful problem useful for Physics Olympiad based on Impulse and Momentum. The Problem: A particle of mass m is made to move with uniform speed v along the perimeter of a regular hexagon. Magnitude of impulse applied at each corner of the hexagon is (a) mv (b) mv√3 (b) mv/2 (d) zero […]
Try this problem from ISI B.Stat, B.Math Subjective Entrance Exam, Problem 4 based on Region close to the center. Problem: Let S be the square formed by the four vertices (1, 1), (1, -1), (-1, 1), and (-1, -1). Let the region R be the set of points inside S which are closer to the […]
Try this beautiful problem from ISI BStat 2017 Subjective 2 based on right-angled triangle in a circle. Understand, solve, and learn.
Problem: Let the sequence \( { a_n} _{n \ge 1 } \) be defined by \(a_n = \tan n \theta \) where \( \tan \theta = 2 \). Show that for all n \( a_n \) is a rational number which can be written with an odd denominator. Discussion: This is simple induction. The claim […]
Here, you will find all the questions of ISI Entrance Paper 2017 from Indian Statistical Institute's B.Stat Entrance. You will also get the solutions soon of all the previous year problems. Problem 1 : Let the sequence \( \{ a_n\} _{n \ge 1 } \) be defined by $$ a_n = \tan n \theta $$ […]
How to Solve a Math Problem? A very common question. Here is how to understand the anatomy of a problem and also why problem-solving is important. Artificial Intelligence, Raychaudhuri Mathematics Award, PreRMO Have you read Polya's 'How to Solve It'? This is a pioneering work on problem-solving strategies. Why is this important? […]
Here are the problems and their corresponding solutions from BStat Hons Objective Admission Test 2005. Try it yourself and then read the solutions.
Dear students, I hope you are doing well. French mathematician Yves Meyer won the Abel Prize for his work in Wavelet theory. You may read more about his work in the words of celebrated mathematician Terence Tao here. Presently I am reading a cult classic by Hilbert: Geometry and Imagination. In introductory […]